The field-driven magnetisation reversal processes in disordered systems exhibit a collective beha... more The field-driven magnetisation reversal processes in disordered systems exhibit a collective behaviour that is manifested in the scale-invariance of avalanches, closely related to underlying dynamical mechanisms. Using the multifractal time series analysis, we study the structure of fluctuations at different scales in the accompanying Barkhausen noise. The stochastic signal represents the magnetisation discontinuities along the hysteresis loop of a 3-dimensional random field Ising model simulated for varied disorder strength and driving rates. The analysis of the spectrum of the generalised Hurst exponents reveals that the segments of the signal with large fluctuations represent two distinct classes of stochastic processes in weak and strong pinning regimes. Furthermore, increased driving rates have a profound effect on the small fluctuation segments and broadening of the spectrum. The study of the temporal correlations, sequences of avalanches, and their scaling features complement...
<p>In each network, nodes represent different scalp locations (labels) while each link indi... more <p>In each network, nodes represent different scalp locations (labels) while each link indicates the positive correlation that exceeds the threshold among the corresponding pair of EEG signals. Remarkably, each connectivity network visually splits into two clusters, which can be identified by the location labels as frontal (upper) and parietal (lower), also confirmed by the community detection analysis. See an example of a larger picture in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g004" target="_blank">Fig 4</a>.</p
<p>Superbrain network of the speaker S2 and the listener <i>L</i><sub>2−3... more <p>Superbrain network of the speaker S2 and the listener <i>L</i><sub>2−3</sub>, illustrating proper coordination, (left), and a weakly connected two-brain structure of the listener <i>L</i><sub>1−4</sub> and the speaker S1, corresponding to wrong coordination (right). Different colour of nodes indicates the identified functional communities. The node’s labels belong to the unique list of 882 scalp locations of all participants; for example, <i>L</i>2<sub>−</sub>3<sub>−</sub><i>TP</i>9 and <i>S</i>2<sub>−</sub><i>F</i>7 indicate the channel “TP9” on the scalp of the listener 3 in group 2, and channel “F7” of the scalp of the speaker S2, respectively. See also the overlaps in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g006" target="_blank">Fig 6</a> and distances in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g008" target="_blank">Fig 8</a> for these pairs.</p
<p>The legend abbreviations: 1Yp001 indicates the first-year network filtered at the level ... more <p>The legend abbreviations: 1Yp001 indicates the first-year network filtered at the level <i>p</i> = 0.01, and so on. Fit lines are according to the discrete generalised beta <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154655#pone.0154655.e008" target="_blank">function (5)</a>; in panel (a) the parameter <i>b</i> = 0.67 ± 0.03 and <i>c</i> varies from 0.32 for 1Yp001 and 0.71 for 2Yp001 to 0.82 for 3Yp001 and 4Yp001, with error bars ±0.03.</p
Similarly to physical and biological systems, diffusive processes are essential for the functioni... more Similarly to physical and biological systems, diffusive processes are essential for the functioning of social systems, in particular, leading to collective behavior, which can be studied from extensive online empirical data. Some examples are the knowledge and innovation diffusion, spreading of news, opinions and diseases or outbreaks of emotion in online social networks. In contrast to physical systems, for example, studies of the domain wall dynamics in random media [1], social dynamics actors live on a graph whose structure evolves with the activity of actors. Moreover, human actors possess specific attributes that affect the diffusion process itself; they can be accounted for by different types of models that go beyond interactions that are standardly considered in physics. Specifically, the adequate approach [2,3] combines methods of statistical physics with agent-based models that are close to the empirical data (from which the action rules and statistical features for agents can be inferred) and graph theory analysis of the underlying social structure. First, we present this concept and define quantities that can be obtained from the online data and simulated by agent-based models.
Predicting the evolution of the current epidemic depends significantly on understanding the natur... more Predicting the evolution of the current epidemic depends significantly on understanding the nature of the underlying stochastic processes. To unravel the global features of these processes, we analyse the world data of SARS-CoV-2 infection events, scrutinising two eight-month periods associated with the epidemic's outbreak and initial immunisation phase. Based on the correlation-network mapping, K-means clustering, and multifractal time series analysis, our results reveal universal patterns, suggesting potential predominant drivers of the pandemic. More precisely, the Laplacian eigenvectors localisation has revealed robust communities of different countries and regions that then cluster according to similar shapes of infection fluctuations. Apart from quantitative measures, the immunisation phase differs significantly from the epidemic outbreak by the countries and regions constituting each cluster. While the similarity grouping possesses some regional components, the appearance...
Exchange of emotional messages between users and between users and a Bot in online chats leads to... more Exchange of emotional messages between users and between users and a Bot in online chats leads to the formation of a directed, weighted complex network. Such type of networks have been studied by mapping the high-resolution empirical data, which are collected from Ubuntu chat channel [1, 2]. In the data, additional information is available in association with the type and the emotional content of exchanged messages. Specifically, machine-learning methods of text analysis were used to classify online chat messages into 13 different dialog act classes, e.g., yes-no question, why question, statement etc. In addition, the exchanged messages were annotated by lexicon-based emotion classifier to extract the emotional valence and arousal from the text of messages [1]. Recently, our analysis of the chat network revealed that a new type of social structure emerges in the self-organized dynamics of chats, which differs significantly from previously studied social networks. Unlike most convent...
Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and ed... more Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.
The interplay between the critical fluctuations and the sample geometry is investigated numerical... more The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a twodimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the timescale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the twodimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.
Physica A: Statistical Mechanics and its Applications, 2004
We study diffusion of information packets on several classes of structured networks. Packets diff... more We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by powerlaws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.
Complexity, Metastability and Nonextensivity, 2005
We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake mo... more We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake model of self-organized criticality. In particular, we consider a 2D square lattice and a random rewiring procedure with a parameter 0 < p < 1 that allows to tune the interaction graph, in a continuous way, from the initial local connectivity to a random graph. The main result is that the OFC model on a small-world topology exhibits self-organized criticality deep within the nonconservative regime, contrary to what happens in the nearest-neighbors model. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents in a wide range of values of the rewiring probability p. The pdf's cutoff can be fitted by a stretched exponential function with the stretching exponent approaching unity within the small-world region.
We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with ... more We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue λ L = 2 of the Laplacian. Further differences between the cyclic modular graphs and trees are found by the statistics of random walks return times and hitting patterns at nodes on these graphs. The distribution of first return times averaged over all nodes exhibits a stretched exponential tail with the exponent σ ≈ 1/3 for trees and σ ≈ 2/3 for cyclic graphs, which is independent on their mesoscopic and global structure.
Physica A: Statistical Mechanics and its Applications, 2001
We introduce and simulate a growth model of the worldwide Web based on the dynamics of outgoing l... more We introduce and simulate a growth model of the worldwide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in-and out-links and for the size of connected component. In a fully grown network of N nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter-average fraction β of updated and added links per time step-towards βc(N) < 10% the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for β ≡ 0, corresponding to the network of science citations.
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networ... more We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges. Scaling in the fluctuations occurs when the dispersion of a quantity at each node or edge increases like the its mean to the power µ. We show that the occurrence of scaling in the fluctuations of both the number of packets passing nodes and the number flowing along edges is related to preferential behaviour in either the topology (in the case of nodes) or in the dynamics (in case the of edges). Within our model the absence of any preference leads to the absence of scaling, and when scaling occurs it is non-universal; for random diffusion the number of packets passing a node scales with an exponent µ which increases continuously with increased acquisition time window from µ = 1/2 at small windows, to µ = 1 at long time windows; In the preferentially navigated diffusive motion, busy nodes and edges have exponent µ = 1, in contrast to less busy parts of the network, where an exponent µ = 1/2 is found. Broad distributions of the return times at nodes and edges illustrate that the basis of the observed scaling is the cooperative behaviour between groups of nodes or edges. These conclusions are relevant for a large class of diffusive dynamics on networks, including packet transport with local navigation rules.
International Journal of Bifurcation and Chaos, 2007
Many transport processes on networks depend crucially on the underlying network geometry, althoug... more Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper, we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low de...
Indian Academy of Sciences – Conference Series, 2017
Mapping time series onto graphs and the use of graph theory methods opens up the possibility to s... more Mapping time series onto graphs and the use of graph theory methods opens up the possibility to study the structure of the phase space manifolds underlying the fluctuations of a dynamical variable. Here, we go beyond the standard graph measures and analyze the higher-order structures such as triangles, tetrahedra and higher-order cliques and their complexes present in the time-series networks, which are detectable by algebraic topology methods. We investigate the Barkhausen noise signal which accompanies domain-wall dynamics during magnetization reversal in weakly disordered ferromagnets by a slow increase of the external field along the hysteresis loop. Our analysis demonstrates how the appearance of the complexes with cliques of a high order correlates to the enhanced collective fluctuations in the central part of the hysteresis loop, where domain-wall depinning occurs. In contrast, the fractional Gaussian noise fluctuations at the beginning of the loop correspond to the graph of a simpler topology. The determined topology measures serve as geometrical indicators of changing dynamical regimes along the hysteresis loop. The multifractal analysis of the corresponding segments of the signal confirms that we deal with different types of stochastic processes.
We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Ola... more We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cutoff region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.
We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall ... more We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low disorder is shown to belong to a class of critical dynamic systems, which are described by a fixed point of the stochastic transport equation with self-consistent disorder correlations.
The field-driven magnetisation reversal processes in disordered systems exhibit a collective beha... more The field-driven magnetisation reversal processes in disordered systems exhibit a collective behaviour that is manifested in the scale-invariance of avalanches, closely related to underlying dynamical mechanisms. Using the multifractal time series analysis, we study the structure of fluctuations at different scales in the accompanying Barkhausen noise. The stochastic signal represents the magnetisation discontinuities along the hysteresis loop of a 3-dimensional random field Ising model simulated for varied disorder strength and driving rates. The analysis of the spectrum of the generalised Hurst exponents reveals that the segments of the signal with large fluctuations represent two distinct classes of stochastic processes in weak and strong pinning regimes. Furthermore, increased driving rates have a profound effect on the small fluctuation segments and broadening of the spectrum. The study of the temporal correlations, sequences of avalanches, and their scaling features complement...
<p>In each network, nodes represent different scalp locations (labels) while each link indi... more <p>In each network, nodes represent different scalp locations (labels) while each link indicates the positive correlation that exceeds the threshold among the corresponding pair of EEG signals. Remarkably, each connectivity network visually splits into two clusters, which can be identified by the location labels as frontal (upper) and parietal (lower), also confirmed by the community detection analysis. See an example of a larger picture in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g004" target="_blank">Fig 4</a>.</p
<p>Superbrain network of the speaker S2 and the listener <i>L</i><sub>2−3... more <p>Superbrain network of the speaker S2 and the listener <i>L</i><sub>2−3</sub>, illustrating proper coordination, (left), and a weakly connected two-brain structure of the listener <i>L</i><sub>1−4</sub> and the speaker S1, corresponding to wrong coordination (right). Different colour of nodes indicates the identified functional communities. The node’s labels belong to the unique list of 882 scalp locations of all participants; for example, <i>L</i>2<sub>−</sub>3<sub>−</sub><i>TP</i>9 and <i>S</i>2<sub>−</sub><i>F</i>7 indicate the channel “TP9” on the scalp of the listener 3 in group 2, and channel “F7” of the scalp of the speaker S2, respectively. See also the overlaps in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g006" target="_blank">Fig 6</a> and distances in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166787#pone.0166787.g008" target="_blank">Fig 8</a> for these pairs.</p
<p>The legend abbreviations: 1Yp001 indicates the first-year network filtered at the level ... more <p>The legend abbreviations: 1Yp001 indicates the first-year network filtered at the level <i>p</i> = 0.01, and so on. Fit lines are according to the discrete generalised beta <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0154655#pone.0154655.e008" target="_blank">function (5)</a>; in panel (a) the parameter <i>b</i> = 0.67 ± 0.03 and <i>c</i> varies from 0.32 for 1Yp001 and 0.71 for 2Yp001 to 0.82 for 3Yp001 and 4Yp001, with error bars ±0.03.</p
Similarly to physical and biological systems, diffusive processes are essential for the functioni... more Similarly to physical and biological systems, diffusive processes are essential for the functioning of social systems, in particular, leading to collective behavior, which can be studied from extensive online empirical data. Some examples are the knowledge and innovation diffusion, spreading of news, opinions and diseases or outbreaks of emotion in online social networks. In contrast to physical systems, for example, studies of the domain wall dynamics in random media [1], social dynamics actors live on a graph whose structure evolves with the activity of actors. Moreover, human actors possess specific attributes that affect the diffusion process itself; they can be accounted for by different types of models that go beyond interactions that are standardly considered in physics. Specifically, the adequate approach [2,3] combines methods of statistical physics with agent-based models that are close to the empirical data (from which the action rules and statistical features for agents can be inferred) and graph theory analysis of the underlying social structure. First, we present this concept and define quantities that can be obtained from the online data and simulated by agent-based models.
Predicting the evolution of the current epidemic depends significantly on understanding the natur... more Predicting the evolution of the current epidemic depends significantly on understanding the nature of the underlying stochastic processes. To unravel the global features of these processes, we analyse the world data of SARS-CoV-2 infection events, scrutinising two eight-month periods associated with the epidemic's outbreak and initial immunisation phase. Based on the correlation-network mapping, K-means clustering, and multifractal time series analysis, our results reveal universal patterns, suggesting potential predominant drivers of the pandemic. More precisely, the Laplacian eigenvectors localisation has revealed robust communities of different countries and regions that then cluster according to similar shapes of infection fluctuations. Apart from quantitative measures, the immunisation phase differs significantly from the epidemic outbreak by the countries and regions constituting each cluster. While the similarity grouping possesses some regional components, the appearance...
Exchange of emotional messages between users and between users and a Bot in online chats leads to... more Exchange of emotional messages between users and between users and a Bot in online chats leads to the formation of a directed, weighted complex network. Such type of networks have been studied by mapping the high-resolution empirical data, which are collected from Ubuntu chat channel [1, 2]. In the data, additional information is available in association with the type and the emotional content of exchanged messages. Specifically, machine-learning methods of text analysis were used to classify online chat messages into 13 different dialog act classes, e.g., yes-no question, why question, statement etc. In addition, the exchanged messages were annotated by lexicon-based emotion classifier to extract the emotional valence and arousal from the text of messages [1]. Recently, our analysis of the chat network revealed that a new type of social structure emerges in the self-organized dynamics of chats, which differs significantly from previously studied social networks. Unlike most convent...
Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and ed... more Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions. Here we use the simplicial complexes description of human connectome, where the shared simplexes encode higher-order relationships between groups of nodes. We study consensus connectome of 100 female (F-connectome) and of 100 male (M-connectome) subjects that we generated from the Budapest Reference Connectome Server v3.0 based on data from the Human Connectome Project. Our analysis reveals that the functional geometry of the common F&M-connectome coincides with the M-connectome and is characterized by a complex architecture of simplexes to the 14th order, which is built in six anatomical communities, and linked by short cycles. The F-connectome has additional edges that involve different brain regions, thereby increasing the size of simplexes and introducing new cycles. Both connectomes contain characteristic subjacent graphs that make them 3/2-hyperbolic. These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.
The interplay between the critical fluctuations and the sample geometry is investigated numerical... more The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a twodimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the timescale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the twodimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.
Physica A: Statistical Mechanics and its Applications, 2004
We study diffusion of information packets on several classes of structured networks. Packets diff... more We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by powerlaws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.
Complexity, Metastability and Nonextensivity, 2005
We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake mo... more We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake model of self-organized criticality. In particular, we consider a 2D square lattice and a random rewiring procedure with a parameter 0 < p < 1 that allows to tune the interaction graph, in a continuous way, from the initial local connectivity to a random graph. The main result is that the OFC model on a small-world topology exhibits self-organized criticality deep within the nonconservative regime, contrary to what happens in the nearest-neighbors model. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents in a wide range of values of the rewiring probability p. The pdf's cutoff can be fitted by a stretched exponential function with the stretching exponent approaching unity within the small-world region.
We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with ... more We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue λ L = 2 of the Laplacian. Further differences between the cyclic modular graphs and trees are found by the statistics of random walks return times and hitting patterns at nodes on these graphs. The distribution of first return times averaged over all nodes exhibits a stretched exponential tail with the exponent σ ≈ 1/3 for trees and σ ≈ 2/3 for cyclic graphs, which is independent on their mesoscopic and global structure.
Physica A: Statistical Mechanics and its Applications, 2001
We introduce and simulate a growth model of the worldwide Web based on the dynamics of outgoing l... more We introduce and simulate a growth model of the worldwide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in-and out-links and for the size of connected component. In a fully grown network of N nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter-average fraction β of updated and added links per time step-towards βc(N) < 10% the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for β ≡ 0, corresponding to the network of science citations.
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networ... more We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges. Scaling in the fluctuations occurs when the dispersion of a quantity at each node or edge increases like the its mean to the power µ. We show that the occurrence of scaling in the fluctuations of both the number of packets passing nodes and the number flowing along edges is related to preferential behaviour in either the topology (in the case of nodes) or in the dynamics (in case the of edges). Within our model the absence of any preference leads to the absence of scaling, and when scaling occurs it is non-universal; for random diffusion the number of packets passing a node scales with an exponent µ which increases continuously with increased acquisition time window from µ = 1/2 at small windows, to µ = 1 at long time windows; In the preferentially navigated diffusive motion, busy nodes and edges have exponent µ = 1, in contrast to less busy parts of the network, where an exponent µ = 1/2 is found. Broad distributions of the return times at nodes and edges illustrate that the basis of the observed scaling is the cooperative behaviour between groups of nodes or edges. These conclusions are relevant for a large class of diffusive dynamics on networks, including packet transport with local navigation rules.
International Journal of Bifurcation and Chaos, 2007
Many transport processes on networks depend crucially on the underlying network geometry, althoug... more Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper, we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low de...
Indian Academy of Sciences – Conference Series, 2017
Mapping time series onto graphs and the use of graph theory methods opens up the possibility to s... more Mapping time series onto graphs and the use of graph theory methods opens up the possibility to study the structure of the phase space manifolds underlying the fluctuations of a dynamical variable. Here, we go beyond the standard graph measures and analyze the higher-order structures such as triangles, tetrahedra and higher-order cliques and their complexes present in the time-series networks, which are detectable by algebraic topology methods. We investigate the Barkhausen noise signal which accompanies domain-wall dynamics during magnetization reversal in weakly disordered ferromagnets by a slow increase of the external field along the hysteresis loop. Our analysis demonstrates how the appearance of the complexes with cliques of a high order correlates to the enhanced collective fluctuations in the central part of the hysteresis loop, where domain-wall depinning occurs. In contrast, the fractional Gaussian noise fluctuations at the beginning of the loop correspond to the graph of a simpler topology. The determined topology measures serve as geometrical indicators of changing dynamical regimes along the hysteresis loop. The multifractal analysis of the corresponding segments of the signal confirms that we deal with different types of stochastic processes.
We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Ola... more We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cutoff region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.
We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall ... more We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low disorder is shown to belong to a class of critical dynamic systems, which are described by a fixed point of the stochastic transport equation with self-consistent disorder correlations.
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Papers by Bosiljka Tadic